Page 275 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

258 V. BARONE ET AL.

lack of any constraint on and < s>. Although the linear term contributes to < a>, it
is, anyway, small and, since in our case <s> and the first derivative of coupling constants
have opposite signs (see appendix), it conterbalances the harmonic contribution. Thus the
resulting correction on < a > is small in all cases. this explains why the static results are
very close to the dynamic ones.

5. Summary and conclusion
The results presented in the preceding sections call for the following general remarks.
i) As noticed in the earliest works on EPR [27,28], all the coupling constants increase,
in absolute value, with the pyramidality at the radical center, the effect being always much
prounounced at the radical enter than at the surrounding atoms.
ii) Vibrational averaging of coupling constants is always operative, but can be masked
by the compensation of effects related to the shape of the potential energy surface from one
side, and of the "property surface" from the other.
iii) From a methodological point of view, standard polarized basis sets and limited CI are
sufficient to computehyperfine coupling constantsoflocalized -radicals, if large amplitude
vibrations are properly taken into account.
The most significant outcome of our study is that a qualitative understanding of vibrational
averaging effects is possible along the line of reasoning developed above. This opens the
opportunity for a more dynamically based analysis of EPR parameters for large non rigid
radicals.

Acknowledgments
The work of V.B. and C.M. was sponsored by the Italian Research Council (CNR
Comitato Informatica), whose support is gratefully acknowledged.

Appendix

Using second order perturbation theory [3], the mean and mean square values of the mass
weighted coordinate s in the vibrational state with quantum number j are explicitely
given by:

where is the harmonic angular frequency